Method and Device for Resolving Collision in a Wireless Telecommunications Network

ABSTRACT

This contention resolution method can be used in a station having a data packet to send in a wireless telecommunications network, which packet is sent (F 100 ) after a predetermined maximum number of selection rounds preceding said sending, said method including, on each of said rounds (k), a step (F 20 ) of drawing a value of a binary random variable (r(k)) representing authorization or prohibition of sending of said packet during said round (k). The probability (p w ) of said binary random variable (r(k)) assuming a predetermined value is adjusted taking into account authorizations and prohibitions of sending said packet obtained by said station during preceding selection rounds (1, . . . , k−1).

BACKGROUND OF THE INVENTION

The present invention relates to wireless telecommunications networks, in particular wireless local access networks (WLAN) conforming to the IEEE 802.11 family of standards.

Such networks are also known as Wi-Fi networks. In many applications they are used to network stations (for example computers, personal digital assistants, and peripherals).

In the document “IEEE 802.11a-1999, IEEE 802.11b-1999, IEEE 802.11d-2001, Part 11: wireless LAN medium access control (MAC) and physical layer (PHY) specifications” the 802.11 standard defines a wireless network traffic regulation method that uses a system of congestion windows (CW) to regulate traffic. According to that standard, in order to determine the time at which to send a data packet, a station draws by chance a random number between 0 and CW−1, the value CW being an integer between two values CW_(min) and CW_(max) specified by the 802.11 standard.

This value CW is counted down to send the packet, the countdown being delayed if the station determines that another station is in the process of sending. Unfortunately, that system using congestion windows causes a large number of collisions in the wireless network, which from the user's point of view are reflected in a great loss of bandwidth.

The document by Z. Abichar and M. Chang, “CONTI: Constant Time Contention Resolution for WLAN Access”, IFIP Networking 2005, below referred to as [CONTI], proposes a constant time contention resolution method that uses a series of successive very short tests to select the station that is going to send.

According to the CONTI method, stations seeking to send are eliminated using a try-bit Boolean variable. To be more precise, each station chooses this variable randomly and sends a signal over the network if the random value is equal to 1, or if not listens to the network. A station withdraws from the network, i.e. decides not to send its data packet during a series of selection rounds, if the binary value is equal to 0 and it detects a signal sent by the other stations.

Although offering better performance than the congestion method defined by the 802.11 standard, the proposed CONTI contention resolution method still causes a high number of collisions in the wireless access network, of the order of 5%.

That problem is caused by the fact that the law of probabilities used for drawing the try-bit random variable is not optimized.

OBJECT AND SUMMARY OF THE INVENTION

The present invention therefore aims to reduce considerably the collisions caused by the CONTI method, by around 15% to 20%, by improving the law of probabilities used for drawing the aforementioned binary random value.

To be more precise, the invention consists in a contention resolution method that can be used in a station having a data packet to send in a wireless telecommunications network, in which method the packet is sent after a predetermined maximum number of selection rounds preceding sending.

This method includes, on each of the selection rounds, a step of drawing a value of a binary random variable representing authorization or prohibition to send the packet during that round.

According to the invention the probability p_(w) of said binary random variable value assuming a predetermined value is adjusted taking into account authorizations and prohibitions to send the packet obtained by the station during preceding selection rounds.

In practice, this resolution method is used simultaneously by a plurality of stations seeking to send a packet in the network. According to the invention, the aforementioned probabilities are adjusted by a mathematical optimization method taking the number of stations into account, which has the advantage of significantly reducing the number of collisions in the wireless telecommunications network compared to prior art contention resolution methods.

In one implementation these probabilities are obtained from the following formula:

$p_{w} = \frac{z_{{\# {(w)}2^{{k\; \max} - {l{(w)}}}} + 2^{{k\; \max} - {l{(w)}} - 1}} - z_{{\# {(w)}2^{{k\; \max} - {l{(w)}}}} + 2^{{k\; \max} - {l{(w)}}}}}{z_{\# {(w)}2^{{k\; \max} - {l{(w)}}}} - z_{{\# {(w)}2^{{k\; \max} - {l{(w)}}}} + 2^{{k\; \max} - {l{(w)}}}}}$

where:

-   -   w represents a binary word (r(1), . . . , r(k−1)) of binary         numeric value #(w) and wherein the binary value of a rank (i) is         equal to said value of the binary random variable (r(i)) drawn         on the selection round (i) corresponding to that rank, I(w)         being the length of the word w;         the values z_(i) being chosen so that:     -   z₀=0; z_(m)=1; 0<z_(i)<z_(i+1)<1, for 1≦i≦m−2, where m=2^(kmax),         kmax being said number of selection rounds, and such that there         exists a positive “density function” h that is normalized         between 0 and 1, such that:

${\int_{zi}^{{zi} + 1}{{h(t)}\ {t}}} = {\frac{1}{m}{\int_{0}^{1}{{h(t)}\ {t}}}}$

This method greatly reduces the number of collisions compared to the prior art CONTI method, as shown below with reference to FIG. 7.

In one implementation, the resolution method of the invention includes a step of defining a scenario consisting in fixing probabilities of a number of stations seeking to send a packet during the same selection round, those stations being referred to as “eligible”, and the value of the density function in the vicinity of 1 is greater the more those probabilities are non-negligible for high values of that number.

In one implementation a characteristic function f of the distribution of the number of eligible stations is defined and the density function h is defined so that it increases with the inflection of the characteristic function.

FIG. 1, which shows the derivative f′ of the characteristic function f in the range [0, 1], explains this choice. It can be shown that the collision rate corresponds to the shaded area between the graphical representation of the curve f′ and its approximation by a Riemann integral.

Consequently, minimizing the collision rate amounts to minimizing this area, namely determining, for a given number of Riemann steps, the position of those Riemann steps (i.e. the points z_(i)) that define the best approximation of f′.

Because of the shape of the representation of the function f′, it is preferable to choose points z_(i) from the range [0, 1] concentrated in the vicinity of 1. This amounts precisely to choosing a function h increasing with the inflection of the characteristic function f, conforming to the following normalization constraint:

∫₀¹h(t) t = 1

The density step function h can be defined on the basis of the points z_(i) as follows, for z_(i)≦x<z_(i+1):

${{h(x)} = \frac{1}{m\left( {z_{i + 1} - z_{i}} \right)}},$

Under these conditions, minimizing the collision rate amounts to minimizing the integral between 0 and 1 of the function that associates x with f″(x)/h(x), where f″, represents the second derivative of the characteristic function f.

The density function h that would minimize the aforementioned integral if h were a continuous function and not a step function is preferably defined as follows:

${h(x)} = {\sqrt{f^{''}(x)}*\frac{1}{{\int_{0}^{1}\sqrt{{f^{''}(t)}{t}}}\ }}$

In one implementation, to obtain the values z_(j):

-   -   a function H is defined as follows:

$\quad\left\{ {\quad\begin{matrix} {{{H(0)} = 0}} \\ {{{H\left( {i + 1} \right)} = {{H(i)} + {h\left( \frac{i + {1/2}}{M} \right)}}}} \end{matrix}} \right.$

where M is a number very much greater than m and z_(j) is defined as follows for 0≦j≦m:

$\quad\left\{ \begin{matrix} {{z_{0} = 0}\mspace{14mu}} \\ {{z_{j} = {\frac{1}{M}\min \left\{ {{i/\frac{H(i)}{H\left( {M - 1} \right)}}\underset{\_}{>}\frac{j}{m}} \right\}}}} \\ {{z_{m} = 1}} \end{matrix} \right.$

This choice of values z_(i) approximates the step function h defined above as closely as possible.

In one implementation, during the scenario definition step, the probabilities k_(n) of a number n of stations seeking to send a packet during the same selection term are fixed as follows:

-   -   k_(n)=1/S for 1≦n≦S; and     -   k_(n)=0 for n>S, where S is the planned number of stations in         the network.

This feature has the advantage of sizing the contention resolution method of a given number of stations.

The number S is chosen as equal to 100, for example.

In one implementation, the steps of the contention resolution method are determined by computer program instructions.

Consequently, the invention is also directed to a computer program on an information medium, adapted to be executed in a station, or more generally in a computer, and including instructions for executing the steps of a resolution method as described above.

This program can use any programming language and take the form of source code, object code or a code that is intermediate between source code and object code, such as a partially compiled form, or any other desirable form.

The invention is also directed to a computer-readable information medium containing instructions of the above computer program.

The information medium can be any entity or device capable of storing the program. For example, the medium can include storage means such as a ROM, for example a CD-ROM or a microelectronic circuit ROM, or magnetic storage means, for example a diskette (floppy disk) or a hard disk.

Furthermore, the information medium can be a transmissible medium such as an electrical or optical signal which can be routed via an electrical or optical cable, by radio or by other means. The program of the invention can in particular be downloaded over an Internet type network.

Alternatively, the information medium can be an integrated circuit incorporating the program and adapted to execute the method in question or to be used in its execution.

In a correlated way, the invention relates to a contention resolution device that can be incorporated into a station having a data packet to send in a wireless telecommunications network. This device includes:

-   -   means for sending said packet after a predetermined maximum         number of selection rounds preceding sending; and     -   means for drawing, in each of the selection rounds, a value of a         binary random variable representing an authorization or a         prohibition to send said packet during that round.

According to the invention the probability p_(w) of said binary random value assuming a predetermined value is adjusted taking into account authorizations and prohibitions to send the packet obtained by the station during preceding selection rounds.

The probabilities p_(w) are stored in a table accessible to a device according to the invention and obtained beforehand from the following equation:

$p_{w} = \frac{z_{\# {(w)}{2^{{kmax} - {l{(w)}}}}^{\;_{+ 2^{{kmax} - {l{(w)}} - l}}}} - z_{\# {(w)}{2^{{kmax} - {l{(w)}}}}^{\;_{+ 2^{{kmax} - {l{(w)}}}}}}}{z_{\# {(w)}2^{{kmax} - {l{(w)}}}} - z_{{\# {(w)}2^{{kmax} - {l{(w)}}}} + 2^{{kmax} - {l{(w)}}}}}$

in which:

-   -   w represents a binary word (r(1), . . . , r(k−1)) of binary         numeric value #(w) and the binary value of rank (i) is equal to         said value of the binary random variable (r(i)) drawn in         selection round (i) that corresponds to that rank;         the values z_(i) being chosen so that:     -   z₀=0; z_(m)=1; 0<z_(i)<z_(i+1)<1, for 1≦i≦m−2, where m=2^(kmax),         kmax being said number of selection rounds, and such that there         exists a positive “density function” h that is normalized         between 0 and 1, such that:

${\int_{zi}^{{zi} + 1}{{h(t)}\ {t}}} = {\frac{1}{m}{\int_{0}^{1}{{h(t)}\ {t}}}}$

The advantages and additional features of the resolution device of the invention are similar to those of the above resolution method and are not repeated here.

BRIEF DESCRIPTION OF THE DRAWINGS

Other features and advantages of the present invention emerge from the description given below with reference to the appended drawings, which illustrate one non-limiting implementation of the invention. In the figures:

FIG. 1, described above, shows the derivative of the characteristic function f in the range [0, 1];

FIG. 2 shows a wireless telecommunications network with a preferred implementation of stations according to the invention;

FIG. 3 shows a preferred embodiment of a contention resolution device of the invention;

FIG. 4 is a flowchart showing the main steps of a preferred implementation of a method of the invention for obtaining a table of probabilities;

FIG. 5 is a flowchart showing the main steps of a preferred implementation of a contention resolution method of the invention;

FIG. 6 shows a tree of probabilities obtained by a contention resolution method of the invention; and

FIG. 7 compares the collision rate obtained by the resolution method of the invention with that obtained by the prior art CONTI method.

FIG. 2 shows a wireless telecommunications network 1 used by stations 10, 10′, 10″ of the invention.

Each of these stations 10 includes a contention resolution device of the invention, described below with reference to FIG. 3.

In the preferred implementation described here, the contention resolution device 100 includes a processor 110, a random-access memory (RAM) 120, a read-only memory (ROM) 130, means 140 for sending and receiving packets and signals in the wireless telecommunications network 1, and a table of probabilities 150.

These elements are interconnected by a bus system (no reference number).

In the example described here, the means 140 for sending and receiving data packets and signals over the wireless telecommunications network 1 consist of a card conforming to the IEEE 802.11 family of standards.

A method of obtaining the table of probabilities 150 is described below with reference to FIG. 4.

During a first step E10, a scenario is defined that fixes the probabilities k_(n) of a number n of stations seeking to send a packet during the same selection round.

In the preferred implementation described here, these probabilities k_(n) are defined as follows:

-   -   k_(n)=1/S for 1≦n≦S; and     -   k_(n)=0 for n>S, where S is the planned number of stations in         the network.

The number S is made equal to 100, for example.

A positive density function h increasing between 0 and 1 is defined during a step E20.

In the preferred implementation described here, this density function h is defined as follows:

h(x)=√{square root over (f″(x))}

where f″ represents the second derivative of a characteristic function f of the distribution of the number of the aforementioned eligible stations.

This function f can be chosen in the form:

${f(x)} = {\sum\limits_{n\underset{\_}{>}1}{k_{n}{x^{n}.}}}$

Then, during a step E30, a tree of probabilities is calculated as follows:

-   -   Firstly, a function H is defined:

$\quad{\quad\left\{ \begin{matrix} {{{H(0)} = 0}} \\ {{{H\left( {i + 1} \right)} = {{H(i)} + {h\left( \frac{i + {1/2}}{M} \right)}}}} \end{matrix} \right.}$

where M is a number very much greater than m and z_(j) is defined for 0≦j≦m as follows:

$\quad\left\{ \begin{matrix} {{z_{0} = 0}} \\ {{z_{j} = {\frac{1}{M}\min \left\{ {{i/\frac{H(i)}{H\left( {M - 1} \right)}}\underset{\_}{>}\frac{j}{m}} \right\}}}} \\ {{z_{m} = 1}} \end{matrix} \right.$

It is possible to verify that the series of z_(i) defined in this way is such that:

${\int_{zi}^{{zi} + 1}{{h(t)}\ {t}}} = {\frac{1}{m}{\int_{0}^{1}{{h(t)}\ {t}}}}$

The probabilities p_(w) are then calculated using the following formula:

$p_{w} = \frac{z_{\# {(w)}2^{{kmax} - {l{(w)}}_{+ 2^{{kmax} - {l{(w)}}}} - l}} - z_{{\# {(w)}2^{{kmax} - {l{(w)}}}} + 2^{{kmax} - {l{(w)}}}}}{z_{\# {(w)}2^{{kmax} - {l{(w)}}}} - z_{{\# {(w)}2^{{kmax} - {l{(w)}}}} + 2^{{kmax} - {l{(w)}}}}}$

in which:

-   -   w is a word in the alphabet {0, 1} in which a “1” of rank i,         respectively a “0” of rank i, represents the fact that said         station has sent, respectively has not sent, said signal in the         selection round i;     -   #(w) represents the numerical value represented by w; and     -   I(w) represents the length of the word w.

Table 1 below represents the probabilities obtained using this implementation of the invention.

TABLE 1 p 0.08 p₁ 0.34 p₀ 0.17 p₁₁ 0.44 p₁₀ 0.40 p₀₁ 0.34 p₀₀ 0.28 p₁₁₁ 0.47 p₁₁₀ 0.47 p₁₀₁ 0.46 p₁₀₀ 0.44 p₀₁₁ 0.43 p₀₁₀ 0.42 p₀₀₁ 0.41 p₀₀₀ 0.36 p₁₁₁₁ 0.49 p₁₁₁₀ 0.48 p₁₁₀₁ 0.49 p₁₁₀₀ 0.48 p₁₀₁₁ 0.48 p₁₀₁₀ 0.48 p₁₀₀₁ 0.47 p₁₀₀₀ 0.47 p₀₁₁₁ 0.46 p₀₁₁₀ 0.46 p₀₁₀₁ 0.46 p₀₁₀₀ 0.46 p₀₀₁₁ 0.46 p₀₀₁₀ 0.45 p₀₀₀₁ 0.44 p₀₀₀₀ 0.42 p₁₁₁₁₁ 0.49 p₁₁₁₁₀ 0.49 p₁₁₁₀₁ 0.49 p₁₁₁₀₀ 0.50 p₁₁₀₁₁ 0.49 p₁₁₀₁₀ 0.49 p₁₁₀₀₁ 0.49 p₁₁₀₀₀ 0.49 p₁₀₁₁₁ 0.49 p₁₀₁₁₀ 0.49 p₁₀₁₀₁ 0.49 p₁₀₁₀₀ 0.49 p₁₀₀₁₁ 0.49 p₁₀₀₁₀ 0.49 p₁₀₀₀₁ 0.48 p₁₀₀₀₀ 0.48 p₀₁₁₁₁ 0.48 p₀₁₁₁₀ 0.48 p₀₁₁₀₁ 0.48 p₀₁₁₀₀ 0.48 p₀₁₀₁₁ 0.48 p₀₁₀₁₀ 0.48 p₀₁₀₀₁ 0.48 p₀₁₀₀₀ 0.48 p₀₀₁₁₁ 0.48 p₀₀₁₁₀ 0.48 p₀₀₁₀₁ 0.48 p₀₀₁₀₀ 0.47 p₀₀₀₁₁ 0.47 p₀₀₀₁₀ 0.47 p₀₀₀₀₁ 0.46 p₀₀₀₀₀ 0.46

FIG. 6 shows this table in the form of a tree for the first three selection rounds. This table should be read as follows:

-   -   the first probability p represents the probability of a station         sending in the first selection round and is the same for all         stations;     -   the probability p₁ represents the probability of drawing the         value “1” for the binary random variable r(k) on the second         selection round given that a value “1” was drawn on the first         selection round;     -   the probability p₀ represents the probability of drawing the         value “1” for the binary random variable r(k) on the second         selection round given that a value “0” was drawn on the first         selection round; and     -   the probability p_(w) represents the probability of drawing the         value “1” for the binary random variable r(k) in the k^(th)         selection round given that the values r(1)r(2)r(k−1) defining         the index w were drawn in the preceding selection round(s).

This table 1 is stored in the table 150 of the contention resolution device 100 of the invention.

The main steps of a contention resolution method of the invention are described next with reference to FIG. 5. It is assumed that this method is implemented by the station 10, which is seeking to send a data packet in the network 1.

During a first step F10, a variable k representing the current selection round is initialized to 1.

This initialization step F10 is followed by a step F20 of drawing a value of a binary random variable r(k).

According to the invention, the probability of this binary random variable r(k) taking the predetermined value “1” on round k is equal to the probability p[r(1), r(2), . . . r(k−1)] read in the table 150.

This step F20 of drawing a random variable value is followed by a step F30 which verifies whether the binary value r(k) drawn is equal to 0.

If so, this test F30 is followed by a step F40 during which the station 10 listens to the wireless telecommunications network to determine if another station 10′, 10″ has sent a signal representing the fact that the other station 10′, 10″ is seeking to send a data packet.

If that signal is detected (result of test F50 positive), the contention resolution method terminates during a step F60 without the station 10 sending its data packet. During this step F60, the station 10 awaits the end of the rounds of selection and sending of a packet by another station 10′, 10″ before returning to the initialization step F10 already described.

Otherwise, if the signal is not detected (result of test F50 negative), this test is followed by a test F80 which determines whether the round k is the last selection round, which amounts to verifying whether the variable k is equal to kmax.

If so, the station 100 sends its data packet during a step F100.

Otherwise, if k is strictly less than kmax, the result of the test F80 is negative. That test is then followed by a step F90 during which the variable k is incremented by one unit.

This incrementation step F90 is followed by the step F20, already described, of drawing a value of a binary random variable r(k) for the next selection round.

If it is determined during the test F30 that the binary value drawn is equal to the predetermined value 1, this test F30 is followed by a step F70 of sending a signal representing the fact that the station 100 is seeking to send a data packet over the network.

This step F70 of sending a signal is followed by the test F80 already described which verifies whether the current selection round k is the last selection round.

If this is so, this test F80 is followed by the step F100 of the station 10 sending the data packet.

Otherwise, if this is not so, the test F80 is followed by the incrementation step F90 already described.

Consider for example table 2, using the notation of the invention, giving the probabilities of sending a data packet by the prior art CONTI method.

TABLE 2 p 0.07 p₁ 0.2 p₀ 0.2 p₁₁ 0.25 p₁₀ 0.25 p₀₁ 0.25 p₀₀ 0.25 p₁₁₁ 0.33 p₁₁₀ 0.33 p₁₀₁ 0.33 p₁₀₀ 0.33 p₀₁₁ 0.33 p₀₁₀ 0.33 p₀₀₁ 0.33 p₀₀₀ 0.33 p₁₁₁₁ 0.4 p₁₁₁₀ 0.4 p₁₁₀₁ 0.4 p₁₁₀₀ 0.4 p₁₀₁₁ 0.4 p₁₀₁₀ 0.4 p₁₀₀₁ 0.4 p₁₀₀₀ 0.4 p₀₁₁₁ 0.4 p₀₁₁₀ 0.4 p₀₁₀₁ 0.4 p₀₁₀₀ 0.4 p₀₀₁₁ 0.4 p₀₀₁₀ 0.4 p₀₀₀₁ 0.4 p₀₀₀₀ 0.4 p₁₁₁₁₁ 0.5 p₁₁₁₁₀ 0.5 p₁₁₁₀₁ 0.5 p₁₁₁₀₀ 0.5 p₁₁₀₁₁ 0.5 p₁₁₀₁₀ 0.5 p₁₁₀₀₁ 0.5 p₁₁₀₀₀ 0.5 p₁₀₁₁₁ 0.5 p₁₀₁₁₀ 0.5 p₁₀₁₀₁ 0.5 p₁₀₁₀₀ 0.5 p₁₀₀₁₁ 0.5 p₁₀₀₁₀ 0.5 p₁₀₀₀₁ 0.5 p₁₀₀₀₀ 0.5 p₀₁₁₁₁ 0.5 p₀₁₁₁₀ 0.5 p₀₁₁₀₁ 0.5 p₀₁₁₀₀ 0.5 p₀₁₀₁₁ 0.5 p₀₁₀₁₀ 0.5 p₀₁₀₀₁ 0.5 p₀₁₀₀₀ 0.5 p₀₀₁₁₁ 0.5 p₀₀₁₁₀ 0.5 p₀₀₁₀₁ 0.5 p₀₀₁₀₀ 0.5 p₀₀₀₁₁ 0.5 p₀₀₀₁₀ 0.5 p₀₀₀₀₁ 0.5 p₀₀₀₀₀ 0.5

On the first selection round, the probability p is used, on the second round the probability p[r(1)], on the third round p[r(1), r(2)], and so on. It is therefore clear that on each selection round the index of the probability used contains as many characters as there have been rounds. Note in the table that, according to [CONTI], and in contrast to the invention, the probabilities for a given selection round (i.e. for two indices that have the same number of characters) are identical, and therefore independent of the station and the value drawn for that station during preceding selection rounds.

FIG. 7 compares the collision rate obtained by the resolution method of the invention with that obtained by the prior art CONTI method, as a function of the number of stations.

Note that the collision rate obtained by the resolution method of the invention (3.5%-5.1%) is lower than that obtained by the CONTI method (4.37%-6.37%).

The contention resolution method and device of the invention therefore reduce the collision rate on the wireless telecommunications network. 

1. A contention resolution method that can be used in a station having a data packet to send in a wireless telecommunications network, comprising determining after a predetermined maximum number of selection rounds whether said station is authorized to send said packet, said method further comprising, on each of said rounds, a step of drawing a value of a binary random variable representing authorization or prohibition to send said packet during said round, and wherein the probability of said binary random variable value assuming a predetermined value is adjusted taking into account authorizations and prohibitions to send said packet obtained by said station during preceding selection rounds.
 2. The contention resolution method according to claim 1, wherein said probability is obtained from the following formula: $p_{w} = \frac{z_{\# {(w)}{2^{{kmax} - {l{(w)}}}}^{\;_{+ 2^{{kmax} - {l{(w)}} - l}}}} - z_{\# {(w)}{2^{{kmax} - {l{(w)}}}}^{\;_{+ 2^{{kmax} - {l{(w)}}}}}}}{z_{\# {(w)}2^{{kmax} - {l{(w)}}}} - z_{{\# {(w)}2^{{kmax} - {l{(w)}}}} + 2^{{kmax} - {l{(w)}}}}}$ where: w represents a binary word (r(1), . . . , r(k−1)) of binary numeric value #(w) and wherein the binary value of a rank (i) is equal to said value of the binary random variable (r(i)) drawn on the selection round (i) corresponding to that rank, I(w) being the length of the word w; the values z_(i) being chosen so that: z₀=0; z_(m)=1; 0<z_(i)<z_(i+1)<1, for 1≦i≦m−2, where m=2^(kmax), kmax being said number of selection rounds, and such that there exists a positive “density function” h that is normalized between 0 and 1, such that: ${\int_{zi}^{{xi} + 1}{{h(t)}\ {t}}} = {\frac{1}{m}{\int_{0}^{1}{{h(t)}\ {t}}}}$
 3. The resolution method according to claim 1, a step of defining a scenario consisting in fixing probabilities of a number of stations seeking to send a packet during the same selection round, said stations being referred to as “eligible”, and the value of said density function depends on said probabilities.
 4. A resolution method according to claim 3, wherein the value of said density function in the vicinity of 1 is greater the more said probabilities are non-negligible for high values of said number.
 5. The resolution method according to claim 4, wherein: a characteristic function of the distribution of the number of said eligible stations is defined; said density function is defined so that it increases with the inflection of said characteristic function.
 6. The resolution method according to claim 5, wherein said density function (h) is defined by: ${h(x)} = {\sqrt{f^{''}(x)}*\frac{1}{\int_{0}^{1}\sqrt{{f^{''}(t)}{t}}}}$ where f″ represents the second derivative of said characteristic function (f).
 7. The resolution method according to claim 3, wherein, during said scenario definition step, said probabilities of a number of stations seeking to send a packet during the same selection round are fixed as follows: k_(n)=1/S for 1≦n≦S; and k_(n)=0 for n>S, where S is the planned number of stations in said network.
 8. The resolution method according to claim 1, wherein, to obtain said values z_(j): a function H is defined as follows: $\quad\left\{ \begin{matrix} {{{H(0)} = 0}} \\ {{{H\left( {i + 1} \right)} = {{H(i)} + {h\left( \frac{i + {1/2}}{M} \right)}}}} \end{matrix} \right.$ where M is a number very much greater than m and z_(j) is defined for 0≦j≦m as follows: $\quad\left\{ \begin{matrix} {{z_{0} = 0}} \\ {{z_{j} = {\frac{1}{M}\min \left\{ {{i/\frac{H(i)}{H\left( {M - 1} \right)}}\underset{\_}{>}\frac{j}{m}} \right\}}}} \\ {{z_{m} = 1}} \end{matrix} \right.$
 9. The resolution method according to claim 1, comprising, in each of said selection rounds: if said drawn binary value is equal to a first predetermined value representing an authorization to send, a step of sending a signal representing the fact that said station is seeking to send a data packet; or if said drawn binary value is equal to a second predetermined value representing a prohibition on sending, a step of listening to said network to determine if another station sent said signal, and where applicable a step of aborting said resolution method without sending said packet.
 10. A contention resolution device that can be incorporated into a station having a data packet to send in a wireless telecommunications network, said device including: means to determine after a predetermined maximum number of selection rounds if said station is authorized to send said packet; and means for drawing, in each of said rounds, a value of a binary random variable representing an authorization or a prohibition to send said packet during said round; wherein the probability of said binary random value assuming a predetermined value is adjusted taking into account authorizations and prohibitions to send said packet obtained by said station during preceding selection rounds, these probabilities being stored in a table accessible by said device.
 11. A station including a resolution device according to claim
 10. 12. A computer program including instructions for executing steps of the resolution method according to claim 1, when said program is executed by a computer.
 13. A computer-readable storage medium storing a computer program comprising instructions for executing the steps of the resolution method according to claim
 1. 